Related papers: Geometric inequalities on Heisenberg groups
We give sufficient conditions for a measured length space (X,d,m) to admit local and global Poincare inequalities. We first introduce a condition DM on (X,d,m), defined in terms of transport of measures. We show that DM, along with a…
In this paper, we derive some important optimal relationships for bi-slant submanifolds in metallic Riemannian product space forms enriching the understanding of their geometric properties and deepening the connection between intrinsic and…
In this note we prove that the Heisenberg group with a left-invariant pseudo-Riemannian metric admits a completely integrable totally geodesic distribution of codimension 1. This is on the contrary to the Riemannian case, as it was proved…
Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary…
With a view towards Riemannian or sub-Riemannian manifolds, RCD metric spaces and specially fractals, this paper makes a step further in the development of a theory of heat semigroup based $(1,p)$ Sobolev spaces in the general framework of…
The main focus of the paper is the investigation of moduli space of left invariant pseudoRiemannian metrics on the cotangent bundle of Heisenberg group. Consideration of orbits of the automorphism group naturally acting on the space of the…
Adams inequalities with exact growth conditions are derived for Riesz-like potentials on metric measure spaces. The results extend and improve those obtained recently on $\mathbb R^n$ by the second author, for Riesz-like convolution…
We study the projection of the left-invariant sub-Riemannian structure on the 3D Heisenberg group $G$ to the Heisenberg 3D nil-manifold $M$ -- the compact homogeneous space of $G$ by the discrete Heisenberg group. First we describe…
We prove a height-estimate (distance from the tangent hyperplane) for $\Lambda$-minima of the perimeter in the sub-Riemannian Heisenberg group. The estimate is in terms of a power of the excess ($L^2$-mean oscillation of the normal) and its…
In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of…
Deformed generalized gauge groups, whch were created from physical considerations and made it possible to clarify some long-standing problems in physics, such as the problem of motion and the problem of the energy of the gravitational…
In Carnot groups of step 2 we consider sets having maximal or minimal possible homogeneous Hausdorff dimension compared to their Euclidean one: in the first case we prove that they must be in a sense vertical, that is a large part of these…
We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a…
Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a Sasakian manifold equipped…
We derive curvature flows in the Heisenberg group by formal asymptotic expansion of a nonlocal mean-field equation under the anisotropic rescaling of the Heisenberg group. This is motivated by the aim of connecting mechanisms at a…
Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian structure and express them using the Riemannian curvature tensor…
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group $\mathbb{H}^n$. The proof is based on a new isoperimetric inequality for closed curves in $\mathbb{R}^{2n}$. We also prove that the…
One of the crucial features of optimal transport on Riemannian manifolds is the equivalence of the `static', original, formulation of the problem and of the `dynamic' one, based on the study of the continuity equation. This furnishes the…
We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric…
In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to…